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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 490049a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
490049.a2 | 490049a1 | \([1, -1, 0, -3033893, 1923796216]\) | \(26250424590620551833/1612113674377913\) | \(189663561676887086537\) | \([2]\) | \(13989888\) | \(2.6429\) | \(\Gamma_0(N)\)-optimal |
490049.a1 | 490049a2 | \([1, -1, 0, -9168448, -8309868435]\) | \(724474288803898839753/165554268658998751\) | \(19477294153462544056399\) | \([2]\) | \(27979776\) | \(2.9894\) |
Rank
sage: E.rank()
The elliptic curves in class 490049a have rank \(0\).
Complex multiplication
The elliptic curves in class 490049a do not have complex multiplication.Modular form 490049.2.a.a
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.